You don't need a barn full of tools to start. A short, good list beats a long, cheap one.
The usual beginner's mistake is buying breadth: a hundred-piece set that covers every eventuality badly. Almost all household furniture repair runs on a handful of items, and the money is far better spent making those few good ones.
Reversible, forgiving and correct for old furniture.
Two or three good ones do most household repairs.
A finish you can renew, not a plastic shell.
The one tool nobody sells and everyone needs.
Start with a simple wooden chair with one loose joint. It is small enough to carry, cheap enough that a mistake doesn't matter, and it teaches the entire core sequence: disassemble, clean, dry-fit, glue, clamp, wait. Refinishing a large tabletop is the classic first project and the classic first disappointment — too much surface, too little margin for error.
Do less than you think you should, then stop and look. Most damage we're asked to undo came from enthusiasm rather than neglect. More about the project behind these notes on the about page.